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There are six different models that are to appear in a fashion show.
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25 Jun 2015, 04:36
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There are six different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?
A. 72 B. 48 C. 64 D. 24 E. 8
Source: Platinum GMAT Kudos for a correct solution.
Re: There are six different models that are to appear in a fashion show.
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25 Jun 2015, 05:13
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Bunuel wrote:
There are six different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?
A. 72 B. 48 C. 64 D. 24 E. 8
Source: Platinum GMAT Kudos for a correct solution.
Since we have 3 continental pairs (EU, SA, NA), these 3 pairs have 3*2*1 = 6 Combinations. Within each pair, you have however 2 different ways to put them together for each of the pair (2*2*2 = 8). So we have 6*8 = 48.
Please correct me if im wrong.
Answer B.
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Re: There are six different models that are to appear in a fashion show.
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25 Jun 2015, 06:28
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Bunuel wrote:
There are six different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?
A. 72 B. 48 C. 64 D. 24 E. 8
Source: Platinum GMAT Kudos for a correct solution.
Let's say that Models of Europe are represented by E1 and E2 respectively
Let's say that Models of South America are represented by S1 and S2
Let's say that Models of North America are represented by Na and N2
So we have to define the total ways of entries of E1 E2 S1 S2 N1 N2
We have to keep E1 E2 together and similarly N1 N2 together and similarly S1 S2 together so make three groups of two models from same region each
Arrangement of these three Group can be done in 3! ways
Arrangement of Models within Group can be done in 2!x2!x2! ways
i.e. Total Ways of Arranging the models so that they are grouped as per region together = (3!)*(2!x2!x2!) = 6*8 = 48
Answer: Option B
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Re: There are six different models that are to appear in a fashion show.
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25 Jun 2015, 06:34
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Bunuel wrote:
There are six different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?
A. 72 B. 48 C. 64 D. 24 E. 8
Source: Platinum GMAT Kudos for a correct solution.
Taking each of the 2 models from 3 continents as one unit , the 3 units can be arranged in 3! ways Also, each of the pairs can be arranged in 2! ways Therefore, total no of ways=3!*3*2!=48 Answer B
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25 Jun 2015, 06:35
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Bunuel wrote:
There are six different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?
A. 72 B. 48 C. 64 D. 24 E. 8
Source: Platinum GMAT Kudos for a correct solution.
Three groups can be arranged way= 3!.. within each group the two models can be arranged in 2! ways .. total ways 3!*2!*2!*2!=48 ans B
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Re: There are six different models that are to appear in a fashion show.
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25 Jun 2015, 06:37
KS15 wrote:
Bunuel wrote:
There are six different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?
A. 72 B. 48 C. 64 D. 24 E. 8
Source: Platinum GMAT Kudos for a correct solution.
Taking each of the 2 models from 3 continents as one unit , the 3 units can be arranged in 3! ways Also, each of the pairs can be arranged in 2! ways Therefore, total no of ways=3!*3*2!=48 Answer B
The highlighted part has calculation mistake 3!*3*2! = 36
I hope it's just a typo error.
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Re: There are six different models that are to appear in a fashion show.
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25 Jun 2015, 09:56
Out of 6 positions, 3 continents can be arranged in 3! Ways=6 Out of those 3 continents each 2 model can be arranged in 2!*2!*2! Ways= 8 So total number of arrangements for models to be arranged for 6 places =6*8=48
There are six different models that are to appear in a fashion show.
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29 Jun 2015, 05:27
Bunuel wrote:
There are six different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?
A. 72 B. 48 C. 64 D. 24 E. 8
Source: Platinum GMAT Kudos for a correct solution.
Platinum GMAT Official Solution:
In this problem, order is important. Jane standing to the left of Mary is a different arrangement than Mary standing to the left of Jane. Because order is important, the permutations equation is used.
The formula for a permutation is: nPr= n!/(n-r)! where n is the total number of selections available and r is the number of items to be selected.
For each set of two models from each continent, there are 2P2ways to arrange them. From the permutation formula with n equal to 2 and r equal to 2 this results in: 2P2= 2! = 2
Since there three groups of two there are: 2P2*2P2*2P2 or 2*2*2 or 8 ways to arrange each group within each group.
Since there are three groups of models that can be placed in three different positions there are: 3P3ways to arrange the three groups.
The value of 3P3is (3*2*1)/(3-3)! = 6/0! = 6, or 6 ways to arrange the different groups. Note that 0! is defined to be equal to one.
Since there are 6 ways to arrange the groups and 8 ways to arrange the models within their own groups there are: 8X6 or 48 different ways to arrange the models.
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08 Jul 2015, 23:25
Bunuel wrote:
There are six different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?
A. 72 B. 48 C. 64 D. 24 E. 8
Source: Platinum GMAT Kudos for a correct solution.
Since Models will sit in pair, So virtually we have 3 place and 3 Pairs to Sit. So three pair can take seat in 3*2 * 1 ways, Each pair has 2 combination so (2*2*2) inter changeable combination within the pair.
Re: There are six different models that are to appear in a fashion show.
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06 Dec 2018, 17:26
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Bunuel wrote:
There are six different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?
A. 72 B. 48 C. 64 D. 24 E. 8
Source: Platinum GMAT Kudos for a correct solution.
Take the task of arranging the models and break it into stages.
Stage 1: Select a model to stand in position #1 There are 6 models to choose from, so we can accomplish this stage in 6 ways.
Stage 2: Select a model to stand in position #2 Since models from the same country must stand together, there's only 1 model who can stand in position #2 So, we can complete this stage in 1 way
Stage 3: Select a model to stand in position #3 There are 4 models remaining, so we can accomplish this stage in 4 ways.
Stage 4: Select a model to stand in position #4 Since models from the same country must stand together, there's only 1 way to complete this stage
Stage 5: Select a model to stand in position #5 There are 2 models remaining, so we can accomplish this stage in 2 ways.
Stage 6: Select a model to stand in position #6 There is only 1 model remaining, so we can accomplish this stage in 1 way.
By the Fundamental Counting Principle (FCP) we can complete all 6 stages (and thus arrange all 6 models) in (6)(1)(4)(1)(2)(1) ways (= 48 ways)
Answer: B
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.